Answer:
The width of rectangle w = 4 units
Step-by-step explanation:
We are given:
Width of rectangle = w
Length of rectangle = w+ 4
Area of rectangle = 32 units
We need to find width of the rectangle
The formula used is: [tex]Area\:of\:rectangle=Length\times Width[/tex]
Putting values and finding width of rectangle
[tex]Area\:of\:rectangle=Length\times Width\\32=(w+4)\times w\\32=w^2+4w\\w^2+4w-32=0[/tex]
We need to solve this quadratic equation to find width (w)
We will use factorisation and break the middle term.
[tex]w^2+4w-32=0\\w^2+8w-4w-32=0\\w(w+8)-4(w+8)=0\\(w-4)(w+8)=0\\w-4=0\:or\:w+8=0\\w=4\:or\:w=-8[/tex]
Since width of rectangle can't be negative, so rejecting w=-8
Therefore, the width of rectangle w = 4 units
